Question

Proving that $\sum\limits^{\infty}_{n=1}\ln\left(1+\frac{x^2}{n^2}\right)$ converges $\forall x \in ℝ$ to a continuous function

score 169 · Answer 1 · 2026-04-15 16:42:57

169

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Proving that $\sum\limits^{\infty}_{n=1}\ln\left(1+\frac{x^2}{n^2}\right)$ converges $\forall x \in ℝ$ to a continuous function

Published on 15 Apr 2026 - 16:42

score 405 · Answer 2 · 2026-04-14 14:31:16

405

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The relation of uniform convergence and exchange of limit

Published on 14 Apr 2026 - 14:31

score 173 · Answer 3 · 2026-04-14 20:32:52

173

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Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{(n+z)^2}$

Published on 14 Apr 2026 - 20:32

score 230 · Answer 4 · 2026-04-16 07:38:59

230

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Uniform convergence of $\frac{1}{x^3}\cos\left(\frac{x}{n}\right)$

Published on 16 Apr 2026 - 7:38

score 37 · Answer 5 · 2026-04-13 22:26:54

37

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Can limit go inside the integral if sequence has only one point of non uniform convergence?

Published on 13 Apr 2026 - 22:26

score 136 · Answer 6 · 2026-04-17 07:06:12

136

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Uniform Convergence of $\langle f_n \rangle = (nx)/(1+n^3x^2)$ for $0 \leq x \leq 1$

Published on 17 Apr 2026 - 7:06

score 54 · Answer 7 · 2026-04-16 06:22:33

54

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Proving a uniformly convergent series is discontinuous over a dense set.

Published on 16 Apr 2026 - 6:22

score 685 · Answer 8 · 2026-04-12 16:54:45

685

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Using Cauchy's Criterion to show non-uniform convergence of series of functions.

Published on 12 Apr 2026 - 16:54

score 257 · Answer 9 · 2026-04-13 21:34:33

257

Views

Uniform convergence of analytic functions on Real subspace yields convergence on open neighbourhood of real subspace

Published on 13 Apr 2026 - 21:34

score 1.1k · Answer 10 · 2026-04-10 21:55:22

1.1k

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Function series and term-by-term derivative

Published on 10 Apr 2026 - 21:55

score 35 · Answer 11 · 2026-04-16 01:58:16

35

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How to prove $f\left( x\right) =\sum^{\infty}_{n=0}\dfrac {1}{2^{n}}\cos\left( 3^{n}x\right)$ converges uniformly on $\mathbb{R}$

Published on 16 Apr 2026 - 1:58

score 95 · Answer 12 · 2026-04-13 14:04:23

95

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Does $f_n$ uniformly converge to $f$?

Published on 13 Apr 2026 - 14:04

score 63 · Answer 13 · 2026-04-13 08:12:28

63

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Uniform convergence of a complex integral

Published on 13 Apr 2026 - 8:12

score 37 · Answer 14 · 2026-04-14 10:24:40

37

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Determine the point wise limit

Published on 14 Apr 2026 - 10:24

score 134 · Answer 15 · 2026-04-14 14:43:12

134

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Proving a sequence converges uniformly

Published on 14 Apr 2026 - 14:43

List Question

Proving that $\sum\limits^{\infty}_{n=1}\ln\left(1+\frac{x^2}{n^2}\right)$ converges $\forall x \in ℝ$ to a continuous function

The relation of uniform convergence and exchange of limit

Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{(n+z)^2}$

Uniform convergence of $\frac{1}{x^3}\cos\left(\frac{x}{n}\right)$

Can limit go inside the integral if sequence has only one point of non uniform convergence?

Uniform Convergence of $\langle f_n \rangle = (nx)/(1+n^3x^2)$ for $0 \leq x \leq 1$

Proving a uniformly convergent series is discontinuous over a dense set.

Using Cauchy's Criterion to show non-uniform convergence of series of functions.

Uniform convergence of analytic functions on Real subspace yields convergence on open neighbourhood of real subspace

Function series and term-by-term derivative

How to prove $f\left( x\right) =\sum^{\infty}_{n=0}\dfrac {1}{2^{n}}\cos\left( 3^{n}x\right)$ converges uniformly on $\mathbb{R}$

Does $f_n$ uniformly converge to $f$?

Uniform convergence of a complex integral

Determine the point wise limit

Proving a sequence converges uniformly

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